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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
79.4-c2 79.4-c \(\Q(\zeta_{13})^+\) \( 79 \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $91212.18964$ 1.49691 \( -\frac{9875329}{79} a^{5} - \frac{4876294}{79} a^{4} + 531385 a^{3} + \frac{23192531}{79} a^{2} - \frac{24136997}{79} a - \frac{6376947}{79} \) \( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( a^{4} + a^{3} - 3 a^{2} - 4 a\) , \( -2 a^{5} + a^{4} + 12 a^{3} - a^{2} - 16 a - 5\bigr] \) ${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(a^{4}+a^{3}-3a^{2}-4a\right){x}-2a^{5}+a^{4}+12a^{3}-a^{2}-16a-5$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.